Stochastic risk

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  • Risk management is a topic on the agenda of an increasing number of organizations around the world for the last 20 years or so. In fact, due to the large number of corporate scandals, risk management has become central in the boardrooms of large enterprises around the world as some stock exchanges in fact demand risk management in the corporate governance work. Despite this, we have a financial crisis that abundantly illustrated that risks were not properly understood – also in corporations that supposedly were conducting risk management....

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  • This book aims to give a complete and self-contained presentation of semi- Markov models with finitely many states, in view of solving real life problems of risk management in three main fields: Finance, Insurance and Reliability providing a useful complement to our first book (Janssen and Manca (2006)) which gives a theoretical presentation of semi-Markov theory. However, to help assure the book is self-contained, the first three chapters provide a summary of the basic tools on semi-Markov theory that the reader will need to understand our presentation.

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  • In this chapter, we study the mathematical structure of a simple one-period model of a financial market. We consider a finite number of assets. Their initial prices at time t = 0 are known, their future prices at time t = 1 are described as random variables on some probability space. Trading takes place at time t = 0. Already in this simple model, some basic principles of mathematical finance appear very clearly. In Section 1.2, we single out those models which satisfy a condition of market efficiency: There are no trading opportunities which yield a profit without any downside risk.

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  • Basic principles underlying the transactions of financial markets are tied to probability and statistics. Accordingly it is natural that books devoted to mathematical finance are dominated by stochastic methods. Only in recent years, spurred by the enormous economical success of financial derivatives, a need for sophisticated computational technology has developed. For example, to price an American put, quantitative analysts have asked for the numerical solution of a free-boundary partial differential equation.

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  • The second result underlines the interest of a two-factor model rather than a one factor model to represent the stochastic dynamics of interest rates. For example, Balduzzi, Das and Foresi (1998) show the presence of a stochastic central tendency in the dynamics of the short and long term interest rates which explains that the level of the short rate is not the only relevant variable to describe its conditional mean.

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  • This Report addresses in considerable detail the consequences of hot particles on and near the skin, in the eye, ear, respiratory system, and gastrointestinal tract. Limits for exposures from hot particles are recommended. If exposures are maintained below the recommended limits, few, if any, deterministic biological effects are expected to be observed, and those effects would be transient in nature. If effects from a hot-particle exposure are observed, the result is an easily treated medical condition involving an extraordinarily small stochastic risk.

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  • The presence of the financial safety net can affect the behaviour of bank stock prices. Explicit provisions such as deposit insurance and the access to liquidity facilities by the central bank, as well as the perceived availability of state support in times of distress, can affect market discipline by numbing creditors’ sensitivity to risk-taking by banks.

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  • This report has been prepared as a result of a request to the National Council on Radiation Protedion and Measurements (NCRP) from the Nuclear Regulatory Commission (NRC). In recent years, nuclear utilities have identified the potential for a limited number of employees to come in contact with microscopic particles that are radioactive. These particles have been given the generic name, independent of their source and particular chemical and radioactive content, of "hot particles."

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  • It is a pleasure to edit the second volume of papers presented at the Mathematical Finance Seminar of New York University. These articles, written by some of the leading experts in financial modeling cover a variety of topics in this field. The volume is divided into three parts: (I) Estimation and Data-Driven Models, (II) Model Calibration and Option Volatility and (III) Pricing and Hedging. The papers in the section on "Estimation and Data-Driven Models" develop new econometric techniques for finance and, in some cases, apply them to derivatives.

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  • Chapter 8 Equilibrium with Complete Markets 8.1. Time- 0 versus sequential trading This chapter describes competitive equilibria for a pure exchange infinite horizon economy with stochastic endowments. This economy is useful for studying risk sharing, asset pricing, and consumption.

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  • This paper provides a review of the methods for measuring portfo- lio performance and the evidence on the performance of profession- ally managed investment portfolios. Traditional performance measures, strongly influenced by the Capital Asset Pricing Model of Sharpe (1964), were developed prior to 1990. We discuss some of the prop- erties and important problems associated with these measures.

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  • This paper develops theory missing in the sizeable literature that uses data envelopment analysis to construct return : risk ratios for investment funds. It explores the production possibility set of the investment funds to identify an appropriate form of returns to scale. It discusses what risk and return measures can justifiably be combined and how to deal with negative risks, and identifies suitable sets of measures. It identifies the problems of failing to deal with diversification and develops an iterative approximation procedure to deal with it.

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  • We build a three-factor term-structure of interest rates model and use it to price corporate bonds. The first two factors allow the risk-free term structure to shift and tilt. The third factor generates a stochastic credit-risk premium. To implement the model, we apply the Peterson and Stapleton (2002) diffusion approximation methodology. The method approximates a correlated and lagged-dependent lognormal diffusion processes. We then price options on credit-sensitive bonds.

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  • We identify and estimate the sources of risk that cause corporate bonds to earn an excess return over default-free bonds. In particular, we estimate the risk premium associated with a default event. Default is modelled using a jump process with stochastic intensity. For a large set of firms, we model the default intensity of each firm as a function of common and firm-specific factors. In the model, corporate bond excess returns can be due to risk premia on factors driving the intensities and due to a risk premium on the default jump risk.

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  • Given the random nature of future events on financial markets, the field of stochastics (prob- ability theory, statistics and the theory of stochastic processes) obviously plays an important role in quantitative risk management. In addition, techniques from convex analysis and opti- mization and numerical methods are frequently being used. In fact, part of the challenge in quantitative risk management stems from the fact that techniques from several existing quanti- tative disciplines are drawn together.

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  • he product of the risk-neutral default intensity and the loss rate equals the instantaneous credit spread. Like Duffee (1999) and Elton et al. (2001), we assume a constant loss rate and allow the default intensity to vary stochastically over time. We model each firm’s default intensity as a function of a low number of latent common factors and a latent firm-specific factor. This extends the analysis of Duffee (1999), who estimates a separate model for each firm. As in Duffee (1999), all factors follow square-root diffusion processes.

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  • We resolve these issues as follows. We show that a nonincreasing returns to scale (nrs) model is usually appropriate when modeling rational choice among investors. We show when multiple risk and return measures can justifiably be combined and identify some suitable measures. We show we need a nonlinear model to justify the assumption of convexity and to model diversification. We develop a method to approximate a solution to this model as accurately as needed using a sequence of linear models. Coherent measures of risk come up again and again in our discussion.

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  • Concerns about stochastic radiogenic risks have led to NRC regulations for diagnostic nuclear medicine that inherently demand a radiation protection philosophy based on the conservative hypothesis that some risk is associated with even the smallest doses of radiation. There is no question that exposure of any individual to potential risk, however low, should be minimized if it can be readily avoided or is not accompanied by some benefit. The weighing of risks and benefits, however, is not always based on objective data and calls for personal value judgments, which can vary widely.

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